cp's OEIS Frontend

A052362 Indices of records in length of English name of n including spaces and dashes (A052360): n such that k < n => A052360(k) < A052360(n).

%I A052362 #25 Jul 12 2022 15:31:07
%S A052362 0,3,11,13,17,21,23,73,101,103,111,113,117,121,123,173,323,373,1101,
%T A052362 1103,1111,1113,1117,1121,1123,1173,1323,1373,3323,3373,11373,13323,
%U A052362 13373,17373,21373,23323,23373,73373,101323,101373,103323,103373,111373,113323,113373,117373
%N A052362 Indices of records in length of English name of n including spaces and dashes (A052360): n such that k < n => A052360(k) < A052360(n).
%C A052362 From _M. F. Hasler_, Aug 12 2020: (Start)
%C A052362 This sequence uses A052360 which counts all characters in the English name of the numbers, including spaces and hyphens, in contrast to A052363 which uses A005589 which only counts the letters. Thus, e.g., "twenty-one" is in this sequence but not in A052363.
%C A052362 It appears that from 1323 on, all terms end in -323 or in -373. After 117(373) these are prefixed by 121, 123, 173, 323, 373 (thousand). Then the next terms is 1'103'323, and after 1'373'373, the next terms are > 3*10^6, then > 11*10^6, etc.
%C A052362 I conjecture that from 103 on all d-digit terms have a smaller (most often but not always (d-1)-digit) term as suffix, and from 173 on they also have an earlier term as prefix. (End)
%e A052362 From _M. F. Hasler_, Aug 12 2020: (Start)
%e A052362 The first term is zero, since all other nonnegative integers (thus certainly all those with longer names) are larger than zero.
%e A052362 "One" and "two" are not in the sequence, since "zero" is smaller but has a longer name.
%e A052362 "Three" is again in the sequence since all smaller numbers (0, 1 and 2) have shorter names. And so on. (End)
%o A052362 (PARI) m=0;for(n=0,2e5, if(m<A052360(n), m=A052360(n); print1(n", "))) \\ _M. F. Hasler_, Aug 12 2020
%o A052362 (Python)
%o A052362 from itertools import count, islice
%o A052362 from num2words import num2words as n2w
%o A052362 def f(n): return len(n2w(n).replace(" and", "").replace(chr(44), ""))
%o A052362 def agen():
%o A052362     record = 0
%o A052362     for n in count(0):
%o A052362         value = f(n)
%o A052362         if value > record: yield n; record = value
%o A052362 print(list(islice(agen(), 46))) # _Michael S. Branicky_, Jul 12 2022
%Y A052362 Cf. A005589, A052360, A052363.
%K A052362 nonn,word,nice,easy
%O A052362 1,2
%A A052362 _Allan C. Wechsler_, Mar 07 2000
%E A052362 Minor edits by _Ray Chandler_, Jul 22 2009
%E A052362 Name and example edited and more terms by _M. F. Hasler_, Aug 12 2020